This question's been bugging me for a very long time! (E) is right, as you know. I see that the Commentator objects to Roehmer using a tactic - impugning the motives of her opponents - and then he uses the same tactic - impugning the motives of his opponent, Roehmer. I think this is descriptively accurate. He doesn't like that Roehmer impugns the motives of her opponents - he says that that style of argumentation will only alienate people who don't already agree with you. But then he turns around and does the same thing by impugning Roehmer's motives saying that oh she doesn't care about alienating people, she's just trying to appeal to her already loyal readers.

I can see how that might make the Commentator unpersuasive, in the same way that a doctor arguing about smoking causes cancer and heart disease while dragging on a cigarette might come across as unpersuasive. But that has nothing to do with the "reasoning" in the argument being "vulnerable to criticism." The doctor probably made a sound argument against smoking. In other words, don't be a hypocrite if you want to persuade people but hypocrites can make valid or sound arguments just like anyone else. This is where I'm stuck. I'm not sure I see how (E) is describing a "vulnerability" in the "reasoning" of the argument.